In the process of filling containers with liquid, it is often necessary to transport the containers in the open state after they have already been filled with the liquid. This need exists, for example, in the area between a filling device and a capping device. For reasons of sales psychology, it is desirable for containers to be filled as full as possible, because the buyer will reject a partially filled container in the belief that it does not contain the full amount promised, even if the container is overdimensioned and the content corresponds exactly to the nominal value. In the case of containers which are filled up to the top or close to the top, however, there is the danger that the liquid can slosh out; that is, some of the nominal content can be lost and, the outside surfaces of the containers and the conveyor device can be contaminated. This danger becomes worse as the transport speed increases and is especially severe in the case of containers with a wide neck such as jars or the wide-neck bottles now coming into more widespread use.